Question

How do you differentiate `y= (5x)/((tanx)(cotx))`?

Answer 1

5

tan x * cot x is simply 1, because cot x equals `1/tan x`. Thus it is y= 5x. Hence `dy/dx` =5

Answer 2

If you don't think first (before you start) you'll use the quotient rule (with the product rule to differentiate the denominator).

Take a few seconds to think, and to ask:
Can I rewrite this before I differentiate to make my life easier?

`tanx = 1/cotx` so `tanx cotx =1`

That means that `y = 5x/1=5x`

So, `y'=5`

Answer 3

`y'=5`

`y=(5x)/((tanx)(cotx)`

As

`tanx=sinx/cosx`

And

`cotx=cosx/sinx`

So,

`y=(5x)/((sinx/cosx)(cosx/sinx))`

`y=(5x)/((cancelsinx/cancelcosx)(cancelcosx/cancelsinx))`

`y=(5x)/1`

`y=(5x)`

Differentiating both sides with respect to 'x'

`y'=5`